You can visualise them as real-world camera filters that can make a photo darker or blurrier.

Or perhaps like a coffee filter, where only water and coffee gets through, and the ground coffee stays behind. Color To Alpha has this effect on pixels, filtering out the pixels of a given colour, and replacing them with transparent ones.

Filters are unique to digital painting in terms of complexity, and their part of the painting pipeline. Some artists only use filters to adjust their colours a little.

Others, using Filter Layers and Filter Masks use them to dynamically update a part of an image to be filtered. This way, they can keep the original underneath, so they don't lose valuable information. This is called 'non-destructive'.